Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
n,m = map(int,input().split())
grid = []
for _ in range(n):
    grid.append(list(map(int,input().split())))

count = 0
moves = []
grid2 = []
for row in grid:
    grid2.append(row[:])


def do_row(grid,row):
    global count
    r = row
    row = grid[row]
    m = min(row)
    count += m
    for _ in range(m):
        moves.append("row " + str(r + 1))
    for idx in range(len(row)):
        row[idx] -= m

def do_rows(grid):
    for r in range(len(grid)):
        do_row(grid,r)

def do_col(grid,col):
    global count
    mcol = min(row[col] for row in grid)
    for _ in range(mcol):
        moves.append("col " + str(col + 1))
    count += mcol
    for row in grid:
        row[col] -= mcol

def do_cols(grid):
    for c in range(len(grid[0])):
        do_col(grid,c)

big = 9999999999999999999999999999999999
def get_count(grid):
    if sum(sum(row) for row in grid) != 0:
        return big
    return count

do_rows(grid)
do_cols(grid)
crc = get_count(grid)
gmoves = moves
moves = []
count = 0
do_cols(grid2)
do_rows(grid2)
ccr = get_count(grid2)
g2moves = moves


ans = min(ccr, crc)
ansmoves = gmoves if ans == crc else g2moves
if ans == big:
    ans = -1
    ansmoves = []
print(ans)
for m in ansmoves:
    print(m)